Recovery analysis for weighted mixed $\ell_2/\ell_p$ minimization with $0<p\leq 1$.
We study the recovery conditions of weighted mixed $\ell_2/\ell_p\,(0<p\leq 1)$ minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. We show that the block $p$-restricted isometry property (RIP) can ensure the robust recovery. Moreover, we present the sufficient and necessary condition for the recovery by using weighted block $p$-null space property. The relationship between the block $p$-RIP and the weighted block $p$-null space property has been established. Finally, we illustrate our results with a series of numerical experiments.
Publisher URL: http://arxiv.org/abs/1709.00257
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